In the last lesson, we learned how to evaluate an arithmetic expression with more than one operation according to the following rules:
|| Rule 1: || Simplify all operations inside parentheses. ||
|| Rule 2: || Perform all multiplications and divisions, working from left to right. ||
|| Rule 3: || Perform all additions and subtractions, working from left to right. ||
However, the problem above includes an exponent, so we cannot solve it without revising our rules.
|| Rule 1: || Simplify all operations inside parentheses. ||
|| Rule 2: || Simplify all exponents, working from left to right. ||
|| Rule 3: || Perform all multiplications and divisions, working from left to right. ||
|| Rule 4: || Perform all additions and subtractions, working from left to right. ||
We can solve the problem above using our revised order of operations.
Problem:
Evaluate this arithmetic expression 18 + 36 ÷ 32
Solution:
18 + 36 ÷32
= 18 + 36 ÷ 9
Simplify all exponents (Rule 2)
18 + 36 ÷ 9
= 18 + 4
Division (Rule 3)
18 + 4
= 22
Addition (Rule 4)
Let's look at some other examples that involve our new rules for order of operations.
Example 1:
Evaluate 52 x 24
Solution:
52 x 24
= 25 x 24
Simplify all exponents, working from left to right (Rule 2)
25 x 24
= 25 x 16
25 x 16
= 400
Multiplication (Rule 3)
Example 2:
Evaluate 289 - (3 x 5)2
Solution:
289 - (3 x 5)2
= 289 - 152
Simplify all operations inside parentheses (Rule 1)
289 - 152
= 289 - 225
Simplify all exponents (Rule 2)
289 - 225
= 64
Subtraction (Rule 4)
Example 3:
Evaluate 8 + (2 x 5) x 34÷ 9
Solution:
8 + (2 x 5) x 34÷ 9
= 8 + 10 x 34÷ 9
Simplify all operations inside parentheses (Rule 1)
8 + 10 x 34÷ 9
= 8 + 10 x 81 ÷ 9
Simplify all exponents (Rule 2)
8 + 10 x 81÷ 9
= 8 + 810 ÷ 9
Perform all multiplications and divisions, working from left to right (Rule 3)
8 + 810 ÷ 9
= 8 + 90
8 + 90
= 98
Addition (Rule 4)
Example 4:
An interior decorator charges $15 per square foot to lay a carpet, and an installation fee of $150. If the room is square and each side measures 12 feet, how much will it cost to carpet it?
Solution:
If one side of the square-shaped room is 12 feet, then the area of the room is (12 feet)2.
15 x 122 + 150
= 15 x 144 + 150
Simplify all exponents (Rule 2)
15 x 144 + 150
= 2,160 + 150
Multiplication (Rule 3)
2,160 + 150
= 2,310
Addition (Rule 4)
Answer:
It will cost $2,310 to carpet this room.
Summary:
To help us remember the order of operations, we can use the mnemonic PEMDAS, which stands for:
Please
Excuse
My
Dear
Aunt
Sally
Parentheses,
Exponents,
Multiplication & Division,
Addition & Subtraction
Note that although there are six words, they correspond to four rules.
Pre/Alg
10/9
- || Rule 1: || Simplify all operations inside parentheses. ||
- || Rule 2: || Perform all multiplications and divisions, working from left to right. ||
- || Rule 3: || Perform all additions and subtractions, working from left to right. ||
However, the problem above includes an exponent, so we cannot solve it without revising our rules.- || Rule 1: || Simplify all operations inside parentheses. ||
- || Rule 2: || Simplify all exponents, working from left to right. ||
- || Rule 3: || Perform all multiplications and divisions, working from left to right. ||
- || Rule 4: || Perform all additions and subtractions, working from left to right. ||
We can solve the problem above using our revised order of operations.Do Exercise on Math Goodies
Work Sheet #3
10/11